#include <bits/stdc++.h>
#define int long long
#define x first
#define y second
#define pb push_back
using namespace std;
using pii=pair <int,int>;
using tii=pair <pii,int>;
int n,m;
vector <pii> g[100010];
vector <int> gg[100010];
bool visited[100010];
vector <int> getdist(int s){
vector <int> dist(n+1,1e18);
dist[s]=0;
for (int i=1; i<=n; i++) visited[i]=0;
priority_queue <pii,vector <pii>,greater <pii> > pq;
pq.push({0,s});
while (!pq.empty()){
pii tp=pq.top(); pq.pop();
if (visited[tp.y]) continue;
visited[tp.y]=1;
for (pii i:g[tp.y]){
if (!visited[i.x]&&tp.x+i.y<dist[i.x]){
dist[i.x]=tp.x+i.y;
pq.push({dist[i.x],i.x});
}
}
}
return dist;
}
vector <int> topo;
void dfs(int cur){
visited[cur]=1;
for (int i:gg[cur]){
if (!visited[i]) dfs(i);
}
topo.pb(cur);
}
void solve(){
int s,t,u,v;
cin>>n>>m>>s>>t>>u>>v;
tii edg[m+1];
for (int i=1; i<=m; i++){
cin>>edg[i].x.x>>edg[i].x.y>>edg[i].y;
g[edg[i].x.x].pb({edg[i].x.y,edg[i].y});
g[edg[i].x.y].pb({edg[i].x.x,edg[i].y});
}
vector <int> ds=getdist(s),dt=getdist(t),du=getdist(u),dv=getdist(v);
for (int i=1; i<=m; i++){
if (ds[edg[i].x.x]+edg[i].y+dt[edg[i].x.y]==ds[t]){
gg[edg[i].x.x].pb(edg[i].x.y);
} else if (ds[edg[i].x.y]+edg[i].y+dt[edg[i].x.x]==ds[t]){
gg[edg[i].x.y].pb(edg[i].x.x);
}
}
for (int i=1; i<=n; i++) visited[i]=0;
for (int i=1; i<=n; i++){
if (!visited[i]) dfs(i);
}
reverse(topo.begin(),topo.end());
bool ok[n+1];
for (int i=1; i<=n; i++) ok[i]=(i==s);
int ans=du[v];
for (int i:topo){
if (!ok[i]) continue;
for (int j:gg[i]){
ok[j]=1;
du[j]=min(du[j],du[i]);
}
ans=min(ans,du[i]+dv[i]);
}
for (int i=1; i<=n; i++) ok[i]=(i==s);
du=getdist(v); dv=getdist(u);
for (int i:topo){
if (!ok[i]) continue;
for (int j:gg[i]){
ok[j]=1;
du[j]=min(du[j],du[i]);
}
ans=min(ans,du[i]+dv[i]);
}
cout<<ans<<'\n';
}
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0);
int t=1;
//cin>>t;
while (t--) solve();
}
